Two-level D-optimal designs for run sizes that are one less than a multiple of four

Two-level orthogonal arrays are known to be D-optimal for main-effects models in the event the number of runs is a multiple of four. Complete catalogs of non-isomorphic orthogonal arrays have been enumerated and investigated to identify those orthogonal arrays that minimize the aliasing between main effects and two-factor interactions and the aliasing among two-factor interactions. In this paper, the focus is on two-level experimental designs involving numbers of runs that are one less than a multiple of four. It turns out that many non-isomorphic D-optimal designs for main-effects models with these numbers of runs can be obtained by dropping one row from an orthogonal array. Some of these designs involve substantially less aliasing than others between the main effects and the two-factor interactions as well as among the two-factor interactions. We explain how we construct non-isomorphic D-optimal designs for main-effects models from complete catalogs of non-isomorphic orthogonal arrays, investigate the differences between these designs, and report the best of them in terms of aliasing.